MinT - Best Known (251−150, 251, s)-Nets in Base 4

Best Known (251−150, 251, s)-Nets in Base 4

(251−150, 251, 104)-Net over F₄ — Constructive and digital

Digital (101, 251, 104)-net over F₄, using

t-expansion [i] based on digital (73, 251, 104)-net over F₄, using
- net from sequence [i] based on digital (73, 103)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 73 and N(F) ≥ 104, using
    - F₆ from the tower of function fields by GarcÃa and Stichtenoth over F₄ [i]

(251−150, 251, 144)-Net over F₄ — Digital

Digital (101, 251, 144)-net over F₄, using

t-expansion [i] based on digital (91, 251, 144)-net over F₄, using
- net from sequence [i] based on digital (91, 143)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 91 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(251−150, 251, 931)-Net in Base 4 — Upper bound on s

There is no (101, 251, 932)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 14 013392 771466 650486 060987 413894 781771 008649 186868 709200 113079 883200 452949 078219 985619 730642 198451 960111 291597 630044 371556 748355 216948 131520 534348 263240 > 4²⁵¹ [i]